Displacement correlations in a two-dimensional colloidal liquid and their relationship with shear strain correlations

TL;DR

This study investigates displacement and shear strain correlations in a 2D colloidal liquid, revealing that displacement correlations exhibit long-range logarithmic behavior indicative of cage effects, providing insights into liquid dynamics.

Contribution

It analytically and numerically demonstrates that displacement correlations are more informative than shear correlations in 2D colloidal liquids, especially regarding long-range behavior.

Findings

Displacement correlations show logarithmic growth with distance.

Displacement correlations reveal long-lived cage effects.

Shear correlations lack this long-range logarithmic behavior.

Abstract

Correlations of the displacement field in a two-dimensional model colloidal liquid is studied numerically and analytically. By calculating the displacement correlations and the shear strain correlations from the numerical data of particle simulations, the displacement field is shown to have nontrivial correlations, even in liquids that are only slightly glassy with the area fraction as low as 0.5. It is suggested analytically and demonstrated numerically that the displacement correlations are more informative than the shear correlations: the former behaves logarithmically with regard to the spatial distance at shorter scales, while the corresponding information is missing from the shear correlations. The logarithmic behavior of the displacement correlations is interpreted as manifesting a long-lived aspect of the cage effect.